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arXiv · 2609.28523

Inequalities for ratios of Gamma functions

Henrik Laurberg Pedersen
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Abstract

We prove that the function $$ \log \frac{Γ(x+a+b)Γ(x)}{Γ(x+a)Γ(x+b)}-b\log\left(1+\frac{a}{x}\right) $$ is a generalized Stieltjes function of order $3$ for $a>0$ and $0 0$ and $b>1$.

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Henrik Laurberg Pedersen. 2026-09-22. Inequalities for ratios of Gamma functions. https://arxiv.org/abs/2609.28523

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